Abstract
In this paper, we investigate the constraints on the total neutrino mass sum m_{nu } in a cosmological model in which dark energy and neutrinos are coupled such that the mass of the neutrinos and potentials are function of the scalar field as m_{nu }=m_{0}exp (frac{alpha phi }{m_{pl}}) and V(phi )=m_{pl}^{4}exp (frac{-lambda phi }{m_{pl}}) respectively. The observational data used in this work include the type Ia supernovae (SN) observation (Pantheon compilation), CC, CMB and BAO data. We find that the neutrino mass is tightly constrained to sum m_{nu }< 0.125 eV 95% Confidence Level (C.L.) and the effective extra relativistic degrees of freedom to be N_{eff}=2.955^{+0.11}_{-0.12} 68% C.L in agreement with the Standard Model prediction N_{eff} = 3.046, matter-radiation equality, z_{eq}=3389^{+24}_{25} (68% C.L). These results are in good agreement with the results of Planck 2018 where the limit of the total neutrino mass is sum m_{nu }<0.12 eV (95% C.L., TT, TE, EE + lowE + lensing + BAO) , N_{eff}=2.99^{+0.17}_{-0.17} (68% C.L., TT, TE, EE + lowE + lensing + BAO) and z_{eq}=3387^{+21}_{21} (68% C.L TT, TE, EE + lowE + lensing + BAO).
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